SOLUTION: i need help on systems of equations with 3 variables. 2x+y-3z=-12 5x-y+z=11 x+3y-2z=-13 Please and Thank you!

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Question 123854: i need help on systems of equations with 3 variables.
2x+y-3z=-12
5x-y+z=11
x+3y-2z=-13
Please and Thank you!
Answer by johnnico6426(16) About Me  (Show Source):
You can put this solution on YOUR website!
There are lot of ways to solve equations with 3 unknown variable. You can do matrices or substitution. For the sake of easiness, I will demonstrate how to solve the 3 equations using substitution.
Equations:
2x%2By-3z=-12
5x-y%2Bz=11
x%2B3y-2z=-13
Isolate the y in the first variable.
y=-2x%2B3z-12
Plug the y in the second equation.
5x-%28-2x%2B3z-12%29%2Bz=11
Simplify.
7x-2z%2B12=11
Isolate z.
z=%287%2F2%29x%2B%281%2F2%29
Plug the z in the y.
y=-2x%2B3%28%287%2F5%29x%2B%281%2F2%29%29-12
Simplify.
y=8.5x-10.5
Plug the NEW y and z value in the last equation.
x%2B3%288.5x-10.5%29-2%28%287%2F2%29x%2B%281%2F2%29%29=-13
Simplify and solve for x.
x=1
Plug x=1 to the new y.
y=8.5%281%29-10.5
y=-2
Plug the y and x value to any of the equations. you should get z=4
Solutions:
x=1
y=-2
z=4